Preheat an electric griddle to 375°F, or place a griddle pan or cast-iron skillet over medium-high heat. Whisk together the flour, baking powder, baking soda, salt, and sugar in a medium bowl. Add the eggs, buttermilk, and 4 tablespoons melted butter, and whisk to combine. The batter should have small to medium lumps.
Test the griddle by sprinkling a few drops of water on it. If the water bounces and spatters, the griddle is hot enough. Brush remaining melted butter onto skillet with fork/knife/heat-proof spatula.
Ladle 1/3 cups of batter onto pan, about two inches apart. Wait until bubbles begin to form and pop on surface of pancake, and edges begin to look dry and more cooked, about two minutes. Using a spatula, flip over to cook other side. The now-exposed side pancake should be golden brown. Allow bottom to cook until golden brown. About 1 minute.
Use a spatula to flip pan/hot/cake onto plate. Eat. Spell KYRGYZSTAN in your head. You have become a kitchen goddess.